Compound Units

Using basic units, the physics unit for velocity are therefore meters per second, written in shorthand m/s. Most physics equations involving velocity will assume that the velocity is in m/s, so you will have to make sure that those are the units you are plugging in. Let's try an exercise in converting unitsof velocity:

The speed limit on a Canadian road is 110 km / hour. Given that 1 mile=1.61 kilometers, find the value of this speed limit in miles per hour. What is the speed in m/s?

110 ~~kilometers~~ /hour X (1 mile/1.61 ~~kilometers~~) = 68.3 mi/hr

Note how, once again, we have arranged things such that the units of kilometers "cancel." Now to the second part:

110 ~~kilometers~~ /hour X (1000 meters/1 ~~kilometers~~) = 110,000 m/hr

110,000 m/hr X (1 ~~hour~~/3600 seconds) = 30.56 m/s

Note how we took things in two separate steps. It takes a little extra writing, but it's worth it to be accurate! Now for some more practice:

How many m/s is 70 miles per hour?

First take care of distance units, then the time units:

70 ~~miles~~/hour X (1.61 ~~kilometers~~/~~mile~~) X (1000 ~~meters~~/~~kilometer~~) =

112700 meters/~~hour~~ X (1 ~~hour~~/3600 seconds) = 31.3 m/s

It's very important to do things methodically, one step at a time. Shortcuts are the surest way to mess something up!

Light travels at 300,000 km/s. What is that speed in m/s and mi/hr?

First do the km to m conversion:

300,000 km/s X (1000 meters/~~kilometer~~) = 300,000,000 m/s

Now go from km to miles and seconds to hours:

300,000 km/s X (1 mile/ 1.61 ~~kilometers~~) X (3600 s/hr)= 670,800,000 mi/hr

It takes you 4 hours to travel 200 miles. On average, how fast were you driving, in mi/hr and in m/s?

Since velocity = change in distance / change in time, the first part is easy:

velocity = 200 miles / 4 hours = 50 mi/hr

For the second part, we have two possile paths. We can take the answer in mi/hr and convert it directly into m/s:

50 mi/hr X (1.61 km/mi) X (1000 m/km) = 80,500 m/hr

80,500 m/hr X (1 hr/3600 s) = 22.36 m/s

Or we can convert the units before we plug them into the equation. like so:

200 ~~miles~~ X (1.61 km/mi) X (1000 m/km) = 322,000 m

4 ~~hours~~ X (3600 sec/hr) = 14,400 sec

velocity = 322,000 m/14,400 s = 22.36 m/s

Either way, we get the same answer. Which way is better? For a simple equation like velocity, it really doesn't matter. However, as a general rule it is a good idea to

convert units before plugging in to an equation!

This is the best way to avoid mistakes, as we shall see in the next section, which deals with the compound units for area and volume.

Questions? Ask the designer, Jim Heath